Direction-of-Arrival Estimation Through Exact Continuous ℓ 2,0 -Norm Relaxation
Emmanuel Soubies, Adilson Chinatto, Pascal Larzabal, João Marcos Travassos Romano, Laure Blanc‐Féraud · IEEE Signal Processing Letters · 2020
On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the ℓ2,0pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the ℓ2,0term with a group minimax concave penalty with suitable parameters. This relaxation is more amenable to non-convex optimization algorithms as it is continuous and admits less local (not global) minimizers than the initial ℓ2,0-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted ℓ2,0algorithm leads to an improved performance over traditional approaches.